The nearest neighbor problem is very common in data science. It's useful in recommender situations but also with neural embeddings in general. It's an expensive thing to calculate so it is common to calculate approximate distances as a proxy. In python a very likeable tool for this is annoy.
All the code below will generate the same plot;
import numpy as np import matplotlib.pylab as plt from annoy import AnnoyIndex columns = 2 vecs = np.concatenate([ np.random.normal(-1, 1, (5000, columns)), np.random.normal(0, 0.5, (5000, columns)), ]) annoy = AnnoyIndex(columns, 'euclidean') for i in range(vecs.shape): annoy.add_item(i, vecs[i, :]) annoy.build(n_trees=1) plt.figure(figsize=(5, 5)) plt.scatter(vecs[:, 0], vecs[:, 1], s=1); indices = annoy.get_nns_by_vector(np.array([-1., -1.]), 2000) subset = vecs[indices, :] plt.scatter(subset[:, 0], subset[:, 1], s=1);
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